On the restricted connectivity and superconnectivity in graphs with given girth

The restricted connectivity @k^'(G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex u has all its neighbors in X; the superconnectivity @k"1(G) is defined similarly, this time considering only vertices u in G-X, hence @k"1(G)= [email protected](G) are given, improving a previous related result by Fiol et al. [Short paths and connectivity in graphs and digraphs, Ars Combin. 29B (1990) 17-31] and guaranteeing @k"1(G)[email protected]^'(G)[email protected](G) under some additional constraints.